A characterizing set (CS) for a deterministic finite state machine (FSM) M is a set of input sequences that, between them, separate (distinguish) all of the states of M. CSs are used within several test generation techniques that return test suites with guaranteed fault detection power. The number of input sequences in a CS directly affects the cost of applying the resultant test suite. In this paper, we study the complexity of decision problems associated with deriving a smallest CS from an FSM, showing that checking the existence of a CS with K sequences is PSPACE-complete. We also consider the length of a CS, which is the sum of the lengths of the input sequences in the CS. It transpires that the problem of deciding whether there is a CS with length at most K is NP-complete. Motivated by these results, we introduce a heuristic to construct a CS, from a deterministic FSM, with the aim of minimizing the number of input sequences. We evaluated the proposed algorithm by assessing its effect when used within a classical test generation algorithm (the W-method). In the evaluation, we used both randomly generated FSMs and benchmark FSMs. The results are promising, with the proposed algorithm reducing the number of test sequences by 37.3% and decreasing the total length of the test suites by 34.6% on average.

确定性有限状态机（FSM）M的特征集（CS）是一组输入序列，在它们之间，分离（区分）M的所有状态。CS用于多种测试生成技术中，这些技术可返回具有保证的故障检测能力的测试套件。CS中输入序列的数量直接影响应用结果测试套件的成本。在本文中，我们研究了与从FSM推导最小CS相关的决策问题的复杂性，表明检查具有K序列的CS的存在是PSPACE-complete。我们还考虑CS的长度，它是CS中输入序列长度的总和。可以看出，确定是否存在一个长度最大为K的CS的问题是NP-complete的。受这些结果的激励，我们引入了一种启发式方法，即从确定性FSM构造CS，以最大程度地减少输入序列的数量。我们通过评估其在经典测试生成算法（W方法）中使用时的效果来评估该算法。在评估中，我们同时使用了随机生成的FSM和基准FSM。结果令人鼓舞，所提出的算法将测试序列的数量减少了37.3％，并将测试套件的总长度平均减少了34.6％。